182

DOCS.

184,

185

JANUARY

1916

are generally

covariant.

I

also contend

that

these

are

the

only equations

that

fulfill

the

following

conditions:

1)

general

covariance.

2)

first order

compons.

Tuv

of matter and

der[ivations]

of

the

gim,s

higher

than

the

second,

do not

appear

in

the

d2gim/dxdxB’s

and

the

energy

tensor.

3)

consistent

with

the

“conservation law”

of

matter

without

any

other

restric-

tions

for

the

Tuv’s.

This

statement is based above all

on

the

knowledge

that

aside from

the

tensors

Gim

and

gim

Z

gaßGaß

aß

there

are no

general

(arbitrary

substitutions

for

covariant)

tensors

(that satisfy

condition

(2)).

Your function G

vanishes

identically,

because-as

you

can

easily

calculate-the

extension

already vanishes,

thus

all

the

more

so

the

divergence

of

the fundamental

tensor

guv(guv).[4]

Hence

it

is

clear

that

a

consideration

according

to

Hamilton’s

principle

would

have

to

be connected

to

the

V-scalar

Q

=

V-9'£9aßGaß,

aß

as

I already

indicated in

yesterday’s

letter.

I

avoided

the

somewhat involved

com-

putation

of the

dq/dguv’s

and

dQ/dgouv’s

by

setting

up

the

tensor

equations directly.

But

the other

way

is

certainly

also workable and

even, more

elegant mathematically.

With

cordial

greetings,

yours,

A.

Einstein.

185. To Paul Ehrenfest

Berlin, Monday,

[24

January 1916

or

later][1]

Dear

Ehrenfest,

Today you

should

finally

be content with

me.

I

am

delighted

about the

great

interest

you are

devoting

to

this

problem.

I

am

not

going

to support

myself

at